Solve y=-0.1(x-11)^2+12.1

$$y = - 0.1 ( x - 11 ) ^ { 2 } + 12.1$$

Solve for y

$$y=x\left(-\frac{x}{10}+2.2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-11\right)^{2}.

$$y=-0.1\left(x^{2}-22x+121\right)+12.1$$

Use the distributive property to multiply -0.1 by x^{2}-22x+121.

$$y=-0.1x^{2}+2.2x-12.1+12.1$$

Add -12.1 and 12.1 to get 0.

$$y=-0.1x^{2}+2.2x$$

Solve for x (complex solution)

$$x=-\sqrt{121-10y}+11$$

$$x=\sqrt{121-10y}+11$$

Solve for x

$$x=-\sqrt{121-10y}+11$$

$$x=\sqrt{121-10y}+11\text{, }y\leq \frac{121}{10}$$